Structure-type formulas for minerals and other inorganic phases

By D.K. SMITH, A.C. ROBERTS, P. BAYLISS, F. LIEBAU
(American Mineralogist, Volume 83, pages 126-132, 1998)

(full text of paper in PDF format, 90 Kb)

This system uses twelve letters to represent cations, anions, and molecules occupying various sites of the structure (site symbols). The letters available as structure-site symbols represent cations with decreasing coordination numbers (CN) as follows:

These definitions leave sufficient remaining letters for other structure-site symbols such as: Structure sites of the same coordination type, yet distinct enough for ordered occupancy of resident cations, may be differentiated by primes (', '',''', etc.).
Variable coordination numbers on a structure site and variable site occupancies are indicated by two symbols or subscripts with the intervening symbol .
For example, the general structure-type formula of amphibole may be written as

A7↔8[T4X11]2X'2

A specific structure-type formula also allows for a mixture of symbols to represent chemical element and structure sites such as:

A0↔1(E'↔G)2G'3G''2[Si4O11]2(OH)2

where as an example of a chemical formula is Ca2Mg5[Si4O11]2(OH)2 for the amphibole TREMOLITE.

Symbols useful for structural details in structure-type formulas

1. For multiple distinct sites in any coordination ' '' '''
2. Indicate the principal radicals involving a single polyhedron or complex in formulas ( )
3. Structural units in formulas involving more than one polyhedral unit [ ]
4. Indicated possible change of coordination numbers between the corresponding symbols and between subscripts to indicate a possible continuous variation between the values
5. Indicates substitution between symbols or subscripts ,
6. Indicates limited substitution between symbols /
7. Indicates chemical substitution within a structure site *
8. Integral subscript or multiplier value hijklmnpqrs
9. Non-integral subscript or multiplier value tuwxyz
10. Indicates inclusive integers in subscripts or multipliers ^
11. For the valence of the cation in subscripts Ú
12. Indicates small deviations from the integer in subscripts such as 1 - δ δ

Note: Vacancies -

Symbols for structural details

In addition to element and structure-site symbols represented by Latin letters, several other symbols (see above) are used to indicate structural details. They are used to indicate the nature of structural units, variations in structure-site occupancy, variations in subscripts and multipliers, and deviations from full occupancy.

Comma. In accord with general usage, the comma "," should be used to indicate continuous substitution, partial as well as complete, if there is no change of CN. Vacancies (symbol ) are treated here just like atoms. This usage is restricted to chemical formulas for atoms on a specific site. The comma is not appropriate for structure site formulas because different symbols indicate a change in the coordination number. Examples for proper use of the comma include forsterite-fayalite [(Mg,Fe)2(SiO4)] and hornblende {(Na, )Ca2(Mg,Fe,Al)5[(Si, Al)4O11]2(OH)2}.. In structure type formulas, the comma is used to mean "or" where substitution may occur. An example is in the zeolites where H2O and M units may both occur.

Slash. The slash "/" between structure-site symbols indicates, without regard to possible solid solubility, that the different atom types form either isotypic members of a structure group or homeotype members of a mineral group. Examples in chemical formulas include the olivine family where (Mg/Fe/Ca/Mn)2(SiO4) implies the isotypic members forsterite, fayalite, larnite, and tephroite and Ca(Ti/Ge)O3 for isotypic perovskite types. Structure-type formulas such as (D/E)GO3 indicate homeotype members of the perovskite group such as Ca[12]Ti[6]O3 and Mg[8]Si[6]O3. The slash is also used for isotypic structures where some of the members have non-LEP elements and other members have LEP-type elements and little, if any, substitution occurs between the two types. An example of this usage is monazite (G/L)(PO4) where the G/L site could be Ca or Pb, which show little tendency to substitute for each other.

Double arrow. The double arrow is used to indicate potential continuous variation between the symbols. This use includes substitution, partial as well as complete, between atoms represented by either element symbol or structure-site symbols where there is a change in CN and the rest of the structure remains equivalent. It is also used in subscripts and multipliers to indicate that continuous variability may occur between the values listed. Its use in subscripts implies the possibility of vacancies in the structure site. If more than a minor part of a structure is affected, the structure would be too different to belong to the same structure-type or homeotype. An example is the augitic pyroxenes where (CaMg,Fe)(Mg,Fe)[Si2O6] indicates that Ca and Mg,Fe may not have the same CN. In structure-type formulas, if the coordination number of a structure site varies continuously with temperature, pressure, or composition, then two structure-site symbols may be used written with an intervening symbol to imply a possible continuous variation in CN, e.g., (DE) and (EG). An example is one of the structure sites in orthopyroxene, which changes CN from 6 to 7 between room temperature and 1200 K as reported by Yang and Ghose (1995). The corresponding structure-type formula is, therefore, written as (EG)G'[T2X6].

Primes. The prime symbols - ', '', ''' are used in general and specific structure-type formulas where different sites may have the same structure-site symbol but distinct characteristics because of different nearest-neighbor arrangements that lead to cation ordering. Examples include amphibole {A01(E G)2G'3G''2[T4O11]2(OH)2} where the sixfold G sites have distinct differences. The first G site may have CN 5, 6, 7 or 8 as a function of composition and temperature; hence, it is written (EG). The other G sites may be occupied by the same cation in some amphibole species and different cations in other amphibole species. Freieslebenite, AgLL'S3, is an example where the L sites have different coordination numbers.

Asterisk. Note in several examples that the primes are used to imply distinct structure sites. Some formulas are written to imply the nature of the chemical substitution within a structure site, i.e., solid solution. To distinguish this chemical substitution, the * symbol may be introduced to indicate the chemical substitution. Thus, the most general formula for the forsterite-fayalite isotype series, (Mg,Fe)2[SiO4], can be represented as GxG*2-x[TX4] or, in more detail, as (GuG*1-u)(GwG*1-w)'[TX4] for a more ordered state. The * symbol should not be used in mineral group structure-type formulas but it is available when it is desirable to make both chemical and structural distinctions.